Bose-Einstein Condensation of Atomic Hydrogen by Dale G

Bose-Einstein Condensation of Atomic Hydrogen by Dale G. Fried B.S. Physics Washington State University (1992) Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 1999 c Massachusetts Institute of Technology 1999. All rights reserved. Author............................................. ................. Department of Physics March 31, 1999 Certified by......................................... ................. Daniel Kleppner Lester Wolfe Professor of Physics Thesis Supervisor Certified by......................................... ................. arXiv:physics/9908044v1 [physics.atom-ph] 22 Aug 1999 Thomas J. Greytak Professor of Physics Thesis Supervisor Accepted by......................................... ................ Thomas J. Greytak Chairman, Department of Physics Graduate Committee Bose-Einstein Condensation of Atomic Hydrogen by Dale G. Fried Submitted to the Department of Physics on March 31, 1999, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract This thesis describes the observation and study of Bose-Einstein condensation (BEC) of magnetically trapped atomic hydrogen. The sample is cooled by magnetic saddlepoint and radio frequency evaporation and is studied by laser spectroscopy of the 1S-2S transition in both the Doppler-free and Doppler-sensitive configuration. A cold collision frequency shift is exploited to infer the density of both the condensate and the non-condensed fraction of the sample. Condensates containing 109 atoms are observed in trapped samples containing 5 1010 atoms. The small equilibrium × condensate fractions are understood to arise from the very small repulsive interac- tion energy among the condensate atoms and the low evaporative cooling rate, both related to hydrogen’s anomalously small ground state s-wave scattering length. Loss from the condensate by dipolar spin-relaxation is counteracted by replenishment from the non-condensed portion of the sample, allowing condensates to exist more than 15 s. A simple computer model of the degenerate system agrees well with the data. The large condensates and much larger thermal reservoirs should be very useful for the creation of bright coherent atomic beams. Several experiments to improve and utilize the condensates are suggested. Attainment of BEC in hydrogen required application of the rf evaporation technique in order to overcome inefficiencies associated with one-dimensional evaporation over the magnetic field saddlepoint which confines the sample axially. The cryogenic apparatus (100 mK) had to be redesigned to accomodate the rf fields of many milli- gauss strength. This required the removal of good electrical conductors from the cell, and the use of a superfluid liquid helium jacket for heat transport. Measurements of heat transport and rf field strength are presented. The rf fields in the apparatus allow rf ejection spectroscopy to be used to measure the trap minimum as well as the temperature of the sample. Thesis Supervisor: Daniel Kleppner Title: Lester Wolfe Professor of Physics Thesis Supervisor: Thomas J. Greytak Title: Professor of Physics Acknowledgments This thesis is dedicated to Jesus Christ, who I understand to be the One who created quantum mechanics, and indeed all of physics and the whole of the entire universe. The extremely rich and subtle complexity of the physical world, and that of quantum systems such as dilute gases at low temperatures and high densities in particular, give me reason to worship Him as an amazing intelligence with creativity and complexity much farther beyond the grasp of the human mind than the physics described in this thesis is beyond the grasp of my sister-in-law’s golden retriever. As I understand it, our Creator’s deep love for us has caused Him to initiate relationship with us, a relationship that has implications far beyond our activities here. For this, too, I worship Him and give to Him my loyalty. He is the King of the Universe. Having gratefully acknowledged the Inventor of the physics studied in this thesis, I also gratefully acknowledge my parents, Ray and Twyla, and my brother, Glenn, who patiently but thoroughly instilled in me a pleasure in working hard, a curiosity about the world, a self-confidence that has allowed me to take risks. Their encouragement and interest during my graduate work has been unwavering, a crucial help when I myself was wavering. As Daniel Kleppner says, one of the important roles of a thesis advisor is to ask a good question. He and my other advisor, Thomas Greytak, have done this superbly. I am grateful to both of them for allowing me to work in their research group and for supporting me financially. Their intellectual commitment to the research and their personal commitment to me as a student have made my years at MIT a pleasure. Much of a graduate education comes through one’s co-workers, and much of the pleasure comes through the camaraderie and friendship in the research group. I am fortunate to have worked with many world-class colleagues during my time at MIT. Mike Yoo, my first office mate, helped me learn practical skills, such as program- ming “makefiles”, and also helped me shoulder responsibilities with confidence. His cheerful insights into graduate student life helped take the edge off all night problem sets. John Doyle, a postdoc when I started in the group, taught me the power of back of the envelope calculations and modeled a systematic, bold approach to solving problems. He has been a continuing encouragement during my graduate career. Jon Sandberg’s helpful ability to teach me the basics of the experiment planted the seed in my head that one day I would be able to run the experiment, too. His confidence in the “younger generation” has helped me push through times of discour- agement. Albert Yu’s cheerily optimistic “there is no problem which cannot be solved” has been my rallying cry more than once. Albert’s friendship is typified by generous hospitality, including one night when he met me after I was mugged on the subway. Claudio Cesar contributed a contagious creativity to the experiment, and a fun demeanor to life in the lab. His optimism and encouragement helped me move toward more of a leadership position. His friendship has helped me maintain perspective. Adam Polcyn joined the experiment the same year I did. Beginning with the finding that our tastes in used books were compatible, I have enjoyed my friendship with him immensely. I often rely on him for reality checks both in my physics and in life. Thomas Killian has been my primary colleague over the most recent several years of work. I learned an intellectual thoroughness from his agile and deep approach to physics. His excitement and engagement with the experiment has made long nights in the lab fruitful and enjoyable. David Landhuis joined the group more recently. His work to rigorously understand physics is very welcome, as is his cheerful willingness to carry out thankless lab chores such as being the safety officer. Dave’s friendship makes work in the lab a pleasure. Stephen Moss, my new office mate, also brings a tenacious quest for deep under- standing to the experiment. His sense of humor, humility, and flexibility are much appreciated. His friendship significantly adds to the fun of working in this research group. Lorenz Willmann, who joined the group two years ago as a postdoc, has taught me about experiment documentation and data analysis. His calm manner has brought a broader perspective to problems that loomed large in my thinking. I am confident of a bright future for this experiment in the capable hands of Dave, Stephen, and Lorenz. Finally, I wish to thank my wife, Diana, for marrying me and giving me her love. I met her three years ago at a French abbey on Easter, while traveling after a physics conference at Les Houches in the French Alps. She has made the last three years of my life meaningful and joyful. I am deeply grateful for her patience and sacrifice during the sometimes long days and nights I have spent in the lab. Contents 1 Introduction 15 1.1 The Lure of Bose-Einstein Condensation . .. 15 1.2 The Significance of the Work in this Thesis . .. 16 1.3 The Basics of Trapping and Cooling Hydrogen . .. 16 2 Theoretical Considerations 21 2.1 DimensionalityofEvaporation . 21 2.2 DegenerateBoseGas ........................... 23 2.2.1 BoseDistribution . .. .. 24 2.2.2 DescriptionoftheCondensate . 26 2.3 Properties of a Bose-Condensed Gas of Hydrogen . ... 28 2.3.1 Relative Condensate Density . 29 2.3.2 Achievable Condensate Fractions . 30 2.3.3 CondensateFeedingRate . 35 2.3.4 Ultimate Condensate Population . 36 3 Implementing RF Evaporation 39 3.1 MagneticHyperfineResonance. 40 3.1.1 HinaStaticMagneticField. 40 3.1.2 HinanRFMagneticField . 42 3.1.3 RF Field Amplitude Requirement . 43 3.1.4 RFCoilDesign .......................... 44 3.2 MechanicalDesignoftheCell . 46 3.2.1 Exclusion of Good Electrical Conductors . 47 3.2.2 DesignoftheSuperfluidJacket . 49 3.3 ConstructionDetails ........................... 53 3.3.1 Materials and Sealing Techniques . 53 3.3.2 Sintering.............................. 54 3.3.3 Bolometer ............................. 55 3.3.4 PressureReliefValve . 55 3.4 MeasurementsofCellProperties. 56 3.4.1 MeasurementsofRFFieldStrength. 56 3.4.2 ThermalConductivity . 57 3.4.3 HeatCapacity........................... 60 3.4.4 RFHeating ............................ 61 7 4 Manipulating Cold Hydrogen by RF Resonance 63 4.1 RFEvaporation.............................. 63 4.1.1 Need for RF Evaporation: Orbits with Long Escape Times .. 63 4.1.2 MixingofEnergy ......................... 65 4.1.3 RF Field Strength Required for Evaporation . 66 4.2 RFEjectionSpectroscopy . 68 4.2.1 Ambiguities of the Trap Dump Technique . 68 4.2.2 Theory of RF Ejection Spectroscopy of a Trapped Gas . 69 4.2.3 BolometricDetection . 71 4.2.4 MeasuringtheTrapBiasField. 73 4.2.5 Measuring the Effective RF Field Strength . 73 4.2.6 Determining the Sample Temperature by RF Ejection Spec- troscopy .............................

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